Advertisements
Advertisements
Question
tan θ cosec2 θ – tan θ is equal to
Options
sec θ
cot2 θ
sin θ
cot θ
Advertisements
Solution
cot θ
Explanation;
Hint:
tan θ cosec2 θ – tan θ = tan θ (cosec2 θ – 1)
= `tan theta xx cot^2 theta`
= `1/cot theta xx cot^2 theta`
= cot θ
APPEARS IN
RELATED QUESTIONS
Prove the following trigonometric identities.
`1/(1 + sin A) + 1/(1 - sin A) = 2sec^2 A`
Prove that
`sqrt((1 + sin θ)/(1 - sin θ)) + sqrt((1 - sin θ)/(1 + sin θ)) = 2 sec θ`
Prove the following identities:
`sqrt((1 - sinA)/(1 + sinA)) = cosA/(1 + sinA)`
Write the value of `(1 + cot^2 theta ) sin^2 theta`.
Prove the following identity :
`(sec^2θ - sin^2θ)/tan^2θ = cosec^2θ - cos^2θ`
prove that `1/(1 + cos(90^circ - A)) + 1/(1 - cos(90^circ - A)) = 2cosec^2(90^circ - A)`
Without using trigonometric identity , show that :
`sec70^circ sin20^circ - cos20^circ cosec70^circ = 0`
If A = 60°, B = 30° verify that tan( A - B) = `(tan A - tan B)/(1 + tan A. tan B)`.
If sinA + sin2A = 1, then the value of the expression (cos2A + cos4A) is ______.
If tan θ + sec θ = l, then prove that sec θ = `(l^2 + 1)/(2l)`.
